The ChemSep Book

Harry A. KooijmanConsultant

Ross TaylorClarkson University, Potsdam, New YorkUniversity of Twente, Enschede, The Netherlands

Libri Books on Demandwww.bod.de

Copyright c© 2000 by H.A. Kooijman and R. Taylor. All rights reserved.

Sample chapter 18 from ISBN 3-8311-1068-9

450

Chapter 18

Design Models for DistillationColumns

This chapter serves as a guide to the correlations inChemSepfor estimating masstransfer coefficients and the pressure drop in distillation (and absorption) columns.The methods used inDesign Modeto determine column design parameters also arediscussed in detail. The chapter ends with the comparison of experimental distillationdata and nonequilibrium model simulations.

18.1 Mass Transfer Coefficient Correlations

Table18.1 provides a summary of the available correlations for trays and packings;the various correlations are discussed in more detail below. Recommended modelsare shown in boldface.

18.1.1 Trays

Binary mass transfer coefficients (MTC’s) can be computed from the Number ofTransfer Units (NTU’s = N) by:

kV = NV /tV aV (18.1)

kL = NL/tLaL (18.2)

451

452

Table 18.1: Available mass transfer coefficient correlations per internals type

Bubble-Cap Sieve Valve Dumped Structuredtray tray tray packing packing

AIChE AIChE AIChE Onda 68 Bravo 85Hughmark Chan-Fair Bravo 82 Bravo 92

Zuiderweg Billet 92 Billet 92Chen-Chuang ... ...

HarrisBubble-Jet

where the vapor and liquid areas are calculated with

aV = ad/εhf (18.3)

aL = ad/αhf (18.4)

the interfacial area density may be estimated from Zuiderweg’s (1982) method (seebelow).

AIChE One of the oldest methods for estimating numbers of transfer units came fromthe AIChE tray efficiency research program of the 1950s. The correlations canbe used for sieve trays, valve trays, and bubble-cap trays.

NV = (0.776 + 4.57hw − 0.238Fs + 104.8QL/Wl)/√

ScV (18.5)

NL = 19700√

DL(0.4Fs + 0.17)tL (18.6)

where

Fs = us

√ρV

t (18.7)

ScV = ηV /ρVt DV (18.8)

tL = hLZWl/QL (18.9)

The clear liquid heighthL is computed from a correlation due to Bennettet al.(1983):

hL = αe

(hw + C(QL/αeWl)0.67

)(18.10)

αe = exp(−12.55(us(ρV /(ρL − ρV ))0.5)0.91) (18.11)

C = 0.50 + 0.438 exp(−137.8hw) (18.12)

453

Chan-Fair The number of transfer units for the vapor phase is:

NV = (10300− 8670FF )FF√

DV tV /√

hL (18.13)

tV = (1− αe)hL/(αeus) (18.14)

The AIChE correlation is used for the number of transfer units for the liquidphase. (hL andαe also are computed with the correlation of Bennettet al.).

ZuiderwegThe vapor phase mass transfer coefficient is

kV = 0.13/ρVt − 0.065/(ρV

t )2 (18.15)

Note thatkV is independent of the diffusion coefficient. The liquid mass trans-fer coefficient is computed from either:

kL = 2.6 10−5(ηL)−0.25 (18.16)

orkL = 0.024(DL)0.25 (18.17)

The interfacial area in the spray regime is computed from:

adhf =40

φ0.3

(U2

s ρVt hLFP

σ

)0.37

(18.18)

and in the froth-emulsion regime from:

adhf =43

φ0.3

(U2

s ρVt hLFP

σ

)0.37

(18.19)

The transition from the spray to mixed froth-emulsion flow is described by:

FP > 3bhL (18.20)

whereb is the weir length per unit bubbling area:

b = Wl/Ab (18.21)

The clear liquid height is given by:

hL = 0.6h0.5w (pFP/b)0.25 (18.22)

Hughmark The numbers of transfer units are given by:

NV = (0.051 + 0.0105Fs)√

ρL

Fs(18.23)

NL = (−44 + 10.7747 104QL/Wl + 127.1457Fs)√

DLAbub/QL (18.24)

454

Harris The numbers of transfer units are given by:

NV =0.3 + 15tG√

ScG

(18.25)

NL =5 + 10tL(1 + 0.17(0.82Fs − 1)(39.3hw + 2))√

ScL

(18.26)

Chen-ChuangThe numbers of transfer units for the vapor is:

tV =hl

us(18.27)

Fs = Us√

ρV (18.28)

NV = 111

η0.1L β0.14

(ρLF 2

s

σ2

)1/3√DV tV (18.29)

and for the liquid

tL =ρL

ρVtV (18.30)

NL = 141

η0.1L β0.14

(ρLF 2

s

σ2

)1/3(V

L

)√DLtL (18.31)

Bubble-JetThis is a combination of a theoretical model described by Taylor and Kr-ishna (1993) and empirical models (Prado, 1986, Prado and Fair, 1990) to de-termine bubble sizes and velocities.

18.1.2 Random Packings

OTO-68 Ondaet al. (1968) [parametersap, dp, σc] developed correlations of masstransfer coefficients for gas absorption, desorption, and vaporization in randompackings. The vapor phase mass transfer coefficient is obtained from

kV = ARe0.7V Sc0.333

V (apDV )(apdp)−2 (18.32)

whereA = 2 if dp < 0.012 andA = 5.23 otherwise. Vapor and liquid veloci-ties are calculated from

uV = V MVw /ρV At (18.33)

uL = LMLw/ρLAt (18.34)

and Reynolds and Schmidt numbers defined by:

ReV =ρV uV

(ηV ap)(18.35)

455

ReL =ρLuL

(ηLap)(18.36)

ScV =ηV

(ρVt DV )

(18.37)

ScL =ηL

(ρLt DL)

(18.38)

The liquid phase mass transfer coefficient is

kL = 0.0051(ReIL)2/3Sc−0.5

L (apdp)0.4(ηLg/ρL)1/3 (18.39)

whereReIL is the liquid Reynolds number based on the interfacial area density

ReIL =

ρLuL

(ηLad)(18.40)

The interfacial area density,ad (m2/m3), is computed from

ad = ap

(1− exp

(−1.45(σc/σ)0.75Re0.1

L Fr−0.05L We0.2

L

))(18.41)

where

FrL =apu

2L

g(18.42)

WeL =ρLu2

L

apσ(18.43)

BF-82 Bravo and Fair (1982) [parametersap, dp, σc] used the correlations of Ondaet al. for the estimation of mass transfer coefficients for distillation in randompackings but proposed an alternative relation for the interfacial area density:

ad = 19.78(CaLReV )0.392√

σH−0.4ap (18.44)

whereH is the height of the packed section andCaL is the capillary number

CaL = uLηL/ρLσ (18.45)

Since the interfacial area density is used in the calculation for the liquid phaseReynolds number the Bravo and Fair method will predict different mass transfercoefficients for the liquid phase.

BS-92 Billet and Schultes (1992) [parametersap, ε, Cfl, Ch, Cp, Cv, Cl] describean advanced empirical/theoretical model which is dependent on the pressuredrop/holdup calculation (Ch, Cp, Cfl). The correlation can be used for both

456

random and structured packings. Vapor and liquid phase coefficients are ad-justed by parametersCv andCl, bringing the total number of parameters tofive. There are trends in the parameters that can be observed from the tabulateddata. Unfortunately, no such generalization was done by Billet, making use ofthe model dependent on the availability of the parameters or experimental data.The mass transfer coefficients are computed from

kL = Cl

(gρl

ηl

)1/6√

DL

dh

(uL

ap

)1/3

(18.46)

kV = Cv

(1√

ε− ht

)√a

dhDV (ReV )3/4(ScV )1/3 (18.47)

with Reynolds and Schmidt numbers calculated as in the method of Ondaet al..The hydraulic diameterdh is

dh = 4ε/ap (18.48)

and the liquid holdup fraction,ht, is calculated as described below under thepressure drop section. The interfacial area density is given by:

ad = ap(1.5/√

apdh)(uLdhρL/ηL)−0.2(u2LρLdh/σ)0.75(u2

L/gdh)−0.45

(18.49)

18.1.3 Structured Packings

BRF-85 Bravoet al. (1985) [parametersap, ε, B, hc, S, Deq, θ] published correla-tions for structured packings. This method is based on the assumption that thesurface is completely wetted and that the interfacial area density is equal to thespecific packing surface:ad = ap. The Sherwood number for the vapor phaseis

ShV = 0.0338Re0.8V Sc0.333

V (18.50)

and is defined by

ShV =kV deq

DV(18.51)

The equivalent diameter of a channel is given by

deq = Bhc [1/(B + 2S) + 1/2S] (18.52)

whereB is the base of the triangle (channel base),S is the corrugation spacing(channel side), andhc is the height of the triangle (crimp height). The vaporphase Reynolds number is defined by

ReV =deqρ

V (uV,eff + uL,eff )ηV

(18.53)

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The effective velocity of vapor through the channel,uV e, is

uV,eff = uV /(ε sin θ) (18.54)

(uV is the superficial vapor velocity,ε the void fraction, andθ the angle of thechannel with respect to the horizontal). The effective velocity of the liquid is

uL,eff =3Γ2ρL

((ρL)2g3ηLΓ

)1/3

(18.55)

whereΓ is the liquid flow rate per unit of perimeter

Γ = ρLuL/P (18.56)

whereP is the perimeter per unit cross-sectional area, computed from

P = (4S + B)/Bhc (18.57)

The penetration model is used to predict the liquid phase mass transfer coeffi-cients with the exposure time assumed to be the time required for the liquid toflow between corrugations (a distance equal to the channel side):

tL = S/uL,eff (18.58)

kL = 2

√DL

πtL(18.59)

BRF-92 Bravo et al. (1992) [parametersap, ε, S, θ, Fse, K2, Ce, dPdzflood] de-veloped a theoretical model for modern structured packings. Four parameterscan be supplied. However, the authors advise using a fixed value for the surfacerenewal correction (Ce), normally0.9. They provide a relation for parameterK2 as well:

K2 = 0.614 + 71.35S (18.60)

The mass transfer calculations depend on the pressure drop and holdup calcu-lation. The effective area can be adjusted with the surface enhancement factorFse, and the liquid resistance with a correction on the surface renewal followingthe penetration model (parameterCe). Effective velocities are computed with

uL,eff =uL

εht sin θ(18.61)

uG,eff =uV

ε(1− ht) sin θ(18.62)

whereht is the fractional liquid holdup (see below at the section on pressuredrop calculation). Reynolds numbers and liquid mass transfer coefficient is nowcalculated as in Bravoet al. (1985) but with

tL = CeS/uL,eff (18.63)

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The vapor phase mass transfer coefficient is obtained from

kV = 0.054(DV

S)Re0.8

V Sc1/3V (18.64)

where the equivalent diameter is replaced with the channel sideS and a differentcoefficient is used. The assumption of a completely wetted packing is dropped.Instead, the interfacial area density is given by

ad = FtFseap (18.65)

Ft =29.12(WeLFrL)0.15S0.359

Re0.2L ε0.6(sin θ)0.3(1− 0.93 cos γ)

(18.66)

wherecos γ is equal to0.9 for σ < 0.0453, otherwise it is computed from

cos γ = 5.211 10−16.835σ (18.67)

Note that a switch point different from that used by Bravoet al. (1992) isemployed to guarantee continuity incos γ.

BS-92 Billet and Schultes (1992) [parametersap, ε, Cfl, Ch, Cp, Cv, Cl] developeda model for both random and structured packings, see the section on randompackings above.

18.2 Pressure Drop Models

There are as many ways to compute tray pressure drops as there to estimate masstransfer coefficients. For packings there is a move away from the use of generalizedpressure drop charts (GPDC) to more theoretically based correlations. We have cho-sen to employ the most recently published models. For packings there are at least 7methods available (see Table18.2). For packings operating above the loading point(FF > 0.7) we advise the use of models that take the correction for the liquid holdupinto account, such as the SBF-89. However, disadvantage is that these models canhave complex (imaginary) solutions, especially at high fractions of flood. This cancause non-cnvergence! The Lev-92 model can be an alternative for it includes a de-pendence on the liquid flow rate to simulate the increased pressure drop at loadingconditions. When the pressure drop is specified as fixed, it is assumed zero.

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Table 18.2: Pressure drop correlations per internals type

Bubble-Cap Sieve Valve Dumped Structuredtray tray tray packing packing

Fixed Fixed Fixed Fixed FixedEstimated Estimated Estimated Ludwig 79 Billet 92

Leva 92 Bravo 86Billet 92 Stichlmair 89

Stichlmair 89 Bravo 92... ...

18.2.1 Tray pressure drop Estimation

The liquid heights on the trays are evaluated from the tray pressure drop calculations.The wet tray pressure drop liquid height is calculated from:

hwt = hd + hl (18.68)

wherehd is the dry tray pressure drop liquid height andhl the liquid height:

hl = hcl + hr +hlg

2(18.69)

The clear liquid height,hcl, is calculated with

hcl = αhw + how (18.70)

where the liquid fraction of the froth,α, is computed with the Barker and Self (1962)correlation:

α =0.37hw + 0.012Fs + 1.78QL/Wl + 0.0241.06hw + 0.035Fs + 4.82QL/Wl + 0.035

(18.71)

The choice of correlation for the liquid fraction turns out to be important as certaincorrelations are dynamically unstable. The height of liquid over the weir,how, iscomputed by various correlations for different types of tray weirs (see Perry’s Hand-book, 1984) and a weir factor (Fw) correction (see Smith, pp. 487) is employed. Forexample for a segmental weir:

how = 0.664Fw

(QL

Wl

)2/3

(18.72)

w =Wl

Dc(18.73)

F 3w =

w2

1− (Fww( 1.68QL

W 2.5l

)2/3 +√

1− w2)2(18.74)

460

whereQL is the volumetric flow over the weir per weir length. The residual height,hr, is only taken into account for sieve trays. Bennett’s method (see Lockett, 1986,pp. 81) is:

hr =(

61.27ρL

)(σ

g

)2/3(ρL − ρV

dh

)1/3

(18.75)

Dry tray pressure,hd, is calculated with:

hd = KρG

ρLu2

h (18.76)

K =ξ

2g(18.77)

where the orifice coefficientξ for sieve trays is computed as described by Stichlmairand Mersmann (1978). For valve trays we use the method of Klein (1982) as describedin Kister (1992, pp. 309–312) whereK is given for the cases with the valves closedor open. It is extended for double weight valve trays as discussed by Lockett (1986,pp. 82–86). The dry tray pressure drop is corrected for liquid fractional entrainment.

The froth density is computed from

hf =hcl

α(18.78)

The liquid gradient,hlg, is estimated from a method due to Fair (Lockett, 1986, pp.72):

Rh =Whf

W + 2hf(18.79)

Uf =QL

Whcl(18.80)

Ref =RhUfρL

ηL(18.81)

f = 7× 104hwRe−1.06f (18.82)

hlg =ZfU2

f

gRh(18.83)

whereW is the average flow-path width for liquid flow, andZ the flow path length.The height of liquid at the tray inlet is:

hi =

√2g

(QL

Wl

)2( 1hcl

− 1hc

)+

2αh2f

3(18.84)

wherehc is the height of the clearance under the downcomer. The pressure loss underdowncomer (expressed as a liquid height) is

hudc =(

12g

)(QL

CdWlhc

)2

(18.85)

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whereCd = 0.56 according to Koch design rules. The height of liquid in the down-comer can now be calculated with the summation:

hdb = hwt + hi + hudc (18.86)

Liquid heights on bubble-cap trays are estimated from a method given in Perry’s(1984) handbook and in Smith (1963). The liquid fraction of the froth is computedaccording to Kastanek (1970).

18.2.2 Random packing Pressure Drop Correlations

For packings the vapor and liquid mass flow per cross sectional area (kg/m2s) andvelocities (m/s) are:

La = LML/At (18.87)

Va = V MV /At (18.88)

uL = La/ρL (18.89)

uV = Va/ρV (18.90)

Lud-79 Ludwig (1979) [parametersA, B] supplied a simple empirical equation forthe pressure drop requiring two fitted parameters (see Wankat, 1988, 420–428):

∆p

∆z= 3.281 242A

(0.2048Va)2

(0.06243ρV )10B(0.06243La) (18.91)

where3.281 242, 0.2048, and0.06243 are conversion factors so that we can useA and B parameters from Wankat. Its accuracy is limited since the influenceof physical properties such as viscosity or surface tension on A and B are notincluded. Even more, the fitted parameters can be flow regime dependent. Theloading regime is not well described with the simple exponential term.

Lev-92 Leva (1992) [parameterFp] devised a modified version of the GeneralizedPressure Drop Correlation (GPDC) presented long ago by Leva (1951). TheGPDC has been the standard design method for decades. Some modificationsthat were actually simplifications made the GPDC lose its popularity. The func-tion worked back from the GPDC and limiting (La = 0) behavior is (in SIunits):

∆p

∆z= 22.3Fp(ηL)0.2φV 2

a

100.035Laφ

gρV(18.92)

with φ = ρwater/ρl = 1000/ρl. This expression is similar to the Ludwig(1979) equation with corrections for the influence of the liquid density and vis-cosity. The only parameter is the packing factorFp that can be obtained from

462

dry pressure drop experiments (see Leva, 1992) or estimated from the specificpacking area over the void fraction cubed. Again, the loading regime is not welldescribed with the simple exponential term. This model is the default methodfor random packings if no model is specified, since it requires only the packingfactor.

SBF-89 Stichlmairet al. (1989) [parametersap, ε, C1, C2, C3] published a semi-empirical method from an analogy of the friction of a bed of particles and thepressure drop. It contains a correction for the actual void fraction corrected forthe holdup, that is dependent on the pressure drop. It is, therefore, an iterativemethod. It is suitable for both random and structured packings, but there arefew published parameters for structured packings. The pressure drop is

∆p

∆z= 0.75f0(1− εp)ρV ∗ U2

V /(dpε4.65p ) (18.93)

where the void fraction of the irrigated bed, equivalent packing diameter, Reynoldsnumber, and friction factor for a single particle are:

εp = ε− ht (18.94)

dp = 6(1− εp)ap (18.95)

ReV = uV dpρV /ηV (18.96)

f0 = C1/ReV + C2/√

ReV + C3 (18.97)

The iterations are started by assuming a dry bed for whichεp = ε and the holdupfraction is computed with the liquid Froude number:

FrL = u2Lap/gε4.65 (18.98)

ht = 0.555Fr1/3L (18.99)

The liquid holdup is limited to0.5 in order to handle flooding.

BS-92 Billet and Schultes (1992) and Billet’s monograph (1979) [parametersa, ε,Cfl, Ch, Cp] include a model with a comprehensive list of packing data andfitted parameters. The method corrects for the holdup change in the loadingregime but employs an empirical exponential term, and is not iterative.

Packing dimension, hydraulic diameter and F-factor are

dp = 6(1− ε)/ap (18.100)

dh = 4ε/ap (18.101)

Fs = uV

√ρV (18.102)

Liquid Reynolds and Froude number are

ReL = uLρL/ηLap (18.103)

FrL = u2Lap/g (18.104)

463

If ReL < 5 thenq = ChRe0.15

L Fr0.1L (18.105)

elseq = 0.85ChRe0.25

L Fr0.1L (18.106)

hl,1 =

(12ηLa2

puL

ρLg

)1/3

(18.107)

hl,2 = hl,1q2/3 (18.108)

hl,fl = 0.3741ε

(ηLρw

ηwρL

)0.05

(18.109)

εfl =(

uL

uV

)√ρL

ρV

(ηL

ηV

)0.2

(18.110)

εfl = g/(C2flε−0.39fl ) (18.111)

uv,fl =√

2g/εfl(ε− hl,fl)1.5√

hl,fl/ap

√ρL/ρV /

√ε (18.112)

if uV > uV,fl thenht = hl,fl else

ht = hl,2 + (hl,fl − hl,2)(uV /uV,fl)13 (18.113)

The pressure drop is then

K1 = 1 + (2/3)(1/1− ε)(dp/Dc) (18.114)

ReV = uV dpρV /(1− ε)ηV K1 (18.115)

φl1 = Cp(64/ReV + 1.8/Re0.08V )

exp(ReL/200)(ht/hl,1)0.3 (18.116)∆p

∆z= φl1(ap/(ε− ht)3)(F 2

s /2)K1 (18.117)

18.2.3 Structured packing Pressure Drop Correlations

BRF-86 Bravo et al. [parametersε, S, sin(θ), C3] compute the pressure drop froman empirical correlation with one fitted parameter, calledC3. This model isunsuitable for pressure drop correlations in the loading regime (FF > 0.7).The pressure drop per height of packing is:

∆p

∆z= (0.171 + 92.7/ReV )(ρV u2

V,eff/deq)(1

(1− C3

√Fr)

)5 (18.118)

464

where

uV,eff = uV /(ε sin θ) (18.119)

ReV =deqρ

V uV,eff

ηV(18.120)

FrL = u2L/deqg (18.121)

SBF-92 Stichlmair et al. (1989) [parametersa, ε, C1, C2, C3] published a semi-empirical method, see the section on pressure drop of random packed columnsabove.

BRF-92 Bravo et al. (1992) [parametersap, ε, S, θ, K2, dPdzflood] developed atheoretical model developed for modern structured packings. Two parametersneed to be supplied for pressure drop calculations, however, theK2 parameterwas fitted by the authors. The pressure of flooding (dPdzflood) can be easilyobtained from data or via Kister’s correlation and the packing factor. The modelincludes an iterative method with a dependence of the liquid holdup on thepressure drop (and vice versa). The Weber, Froude, and Reynolds numbers are

WeL = u2LρLS/σ (18.122)

FrL = u2L/(Sg) (18.123)

ReL = uLSρL/ηL (18.124)

The effectiveg (as a function ofht) is obtained from:

geff =(

1− dPdZ

dPdZflood

)(ρL − ρV )

ρLg (18.125)

ThenFt (see above),ht, and dPdZ are computed

ht =(

4Ft

S

)2/3( 3ηLuL

ρV sin θεgeff

)1/3

(18.126)

A =0.177ρV

Sε2(sin θ)2(18.127)

B =88.774ηV

S2ε sin θ(18.128)

∆p

∆z= (Au2

V + BuV )(

11−K2ht

)5

(18.129)

The calculation is repeated until pressure drop converges or when it becomeslarger than the pressure drop at flood. There can be problems converging thismethod.

BS-92 Billet and Schultes (1992) and Billet’s monograph (1979?) [ap, ε, Cf l, Ch,Cp] See the section on pressure drop of random packed columns above.

465

18.3 Entrainment and Weeping

Entrainment and weeping flows (for trays only) change the internal liquid flows andinfluence the performance of the column internals.ChemSep currently does notsupport the handling of these flows. This is due to the fact that few entrainmentmodels behave properly. Neither is the effect of the entrainment and weeping flowson the mass transfer properly taken into account.

Entrainment can be estimated from the fractional liquid entrainment from Hunt’s cor-relation and from Figure 5.11 of Lockett (1986) for sieve trays:

φL = 7.75 10−5

(0.073

σ

)Mv

(Uv

Ts − 2.5hcl

)3.2

(18.130)

The weep factor is estimated from a figure from Smith (1963, p. 548), that was fittedto the following correlation

WF =0.135 φ ln(34(Hw + How) + 1)

(Hd + Hr)(18.131)

whereφ is the open area ratio.

18.4 Packing Flooding and Minimum Wetting

The fraction of flooding for packings is computed by dividing the superficial gas ve-locity by the gas velocity at flood. The latter is found in an iterative process from thepressure drop correlation (keeping the liquid to vapor ratio constant!) and the speci-fied pressure drop of flood. If no flood pressure drop is specified it is computed fromthe packing factor with the Kister and Gill correlation. If no pressure drop model isselected, the Leva’s method is used, which also has the packing factor as only param-eter.

The minimum operating conditions, similar to the weep point for tray operation, is setto the minimum wetting rate predicted by Schmidt (1979). Schmidt calculates a liquidfalling number

CL = 1633.6(0.062428ρL)(1000σ)3/(1000ηL)4 (18.132)

and the minimum wetting rate is (inUSgal/min/ft2):

QMW =0.3182C

2/9L (1− cos φ)2/3√

(1− TL)ap/0.3048(18.133)

466

whereφ is the liquid contact angle andTL is the shear stress number:

TL = 0.9FF−2.8 (18.134)

with FF as the fraction of flood. The contact angle for metals is10o (0.1745 rad).To obtain contact angles for other packings the contact angle is assumed inverse pro-portional to the critical surface tension,σc. For metals we haveσc = 0.075, so thecontact angle is computed with

φ = 0.1745(

0.075σc

)(18.135)

With this approach we obtaim higher minimum wetting rates for plastic packings thanfor metal packings. The minimum operating or ‘weep’ fractionWF is then taken as

WF =QMW

uL(18.136)

whereuL is the superficial liquid flow.

18.5 Column Design

Tray layout parameters that specify a complete design (for the calculation of masstransfer coefficients and pressure drops) are shown in Table18.3. For packings onlythe column diameter and bed height are design parameters, other parameters (such asvoid fraction, nominal packing diameter, etc.) are fixed once the type of packing hasbeen selected. The packed bed height must be specified since it determines the desiredseparation and the capacity.

A very important parameter in tray column design is the system factor (SF). It repre-sents the uncertainty in design correlations with regard to phenomena that are currentlystill not properly modeled, such as foaming.

Different design methods can be employed:

Fraction of flooding; this is the standard design method for trays, we have employeda modified version of the method published by Barnicki and Davis (1989).

Pressure drop; this is the usual design method for packed columns, but is very usefulas well for tray design with pressure drop constraints.

other design methods can be thought of: ones that minimize pressure drop and cost,or maximize flexibility and efficiency.ChemSephas a modular structure to allowdifferent design methods to be implemented.

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Table 18.3: Tray layout data

General (sieve) tray layout data:Column diameter Active areaNumber of flow passes Total hole areaTray spacing Downcomer areaLiquid flow path length Weir lengthHole diameter Weir heightHole pitch Deck thicknessDowncomer clearanceAdditional data for bubble caps:Cap diameter Slot areaSlot height Riser areaSkirt clearance Annual areaAdditional data for valves:Closed Loss K Open Loss KEddy Loss C Ratio Valve LegsValve Density Valve ThicknessFraction Heavy Valves Heavy Valve Thickness

18.5.1 Tray Column Design: Fraction of flooding

The first task in this approach to tray design is to assign all layout parameters to con-sistent values corresponding to the required capacity defined by the fraction of flood-ing and current flowrates. These defaults function as starting points for subsequentdesigns.

The initial free area ratio is taken to be 15% of the active area. The active area is de-termined from a capacity factor calculation with internals specific methods (for sieveand bubble-cap trays the default is Fair’s correlation by Ogboja and Kuye (19), andthe Glitsch method is used for valve trays). The tray spacing is initially set to thedefault value (of0.5m) and the downcomer area is calculated according to a methodin the Glitsch manual (limited by a minimum time residence check). From the com-bined areas the column diameter is computed. The number of liquid passes on a trayis initially set by the column diameter; under5ft one pass, under8ft two,10ft three,under13ft four, else five passes. With the number of passes and the column diameterthe total weir length is computed. Once the weir length is determined the liquid weirload is checked, if too high the number of passes is incremented and a new weir lengthis evaluated until the weir load is below a specified maximum.

468

Initial weir height is taken as 2”, but limited to a maximum of 15 % of the tray spacing.For notched or serrated weirs the notch depth is a third of the weir height. For serratedweirs the angle of serration is45o. Circular weirs have diameters 0.9 times the weirlength. The hole diameter is set to 3/16” for sieve trays and tray thickness 0.43 timesthe hole diameter (or 1/10”). The hole pitch is computed from the free area ratio andhole diameter according to a triangular pitch. The default downcomer clearance is 1.5”but is limited by the maximum allowed downcomer velocity according to the Glitchmethod, de-rated with the system factor. The clearance is set to be at least 0.5” lowerthan the weir height to maintain a positive liquid seal but is limited to a minimum of0.5”.

For bubble-cap trays the cap diameter is 3” for column diameters below 4.5ft and4” for above. The hole diameter can vary between 60% to 71% of the cap diameter,and default taken as 70%. Default skirt clearance is 1” with minimum of 0.5” andmaximum of 1.5”. The slot height can vary in between 0.5” and 1.5”, where thedefault is 1” for cap diameters below 3.5” and 1.25” for larger cap diameters. Thepitch can vary from 1.25” to half the flow path length (minimum number of rows istwo), with the default value set to 1.25”.

Valve trays are initialized to be Venturi orifice uncaged, carbon steel valves of 3mm

thick with 3 legs (see Kister, 1992, p312). The hole diameter is 1” for column smallerthan 4.5ft, otherwise 2”. No double weight valves are present.

The second task in the fraction of flooding method consists of finding the proper freearea ratio (β = Ah/Ab = hole area / active area) so that no weeping occurs. Thisratio can vary between a minimum of 5% (for stable operation) and a maximum of20%. To test whether weeping occurs, we use the correlation of Lockett and Banik(1984):Frhole > 2/3. The method requires all liquid heights to be evaluated at weeprate conditions. This task is ignored for bubble-cap trays. The weep test is done atweeping conditions, with a weep factor at 60 % (this can be changed). Calculation ofthe liquid heights was described in Section18.2. If weeping occurs at the lower boundfor the free area ratio, a flag is set for the final task to adapt the design.

The final task consists of evaluating all liquid heights at normal conditions and to doa number of checks:

• vapor distribution (for bubble-cap trays),

• weeping (for sieve trays/valve trays),

• hydraulic flooding,

• excessive liquid entrainment,

469

• froth height limit, and

• excessive pressure drop

If a check fails, the design is modified to correct the problem, according to the ad-justments shown in Table18.4after which new areas are calculated from the capacitycorrelations. Part of this task is also to keep the layout parameters within certainbounds to maintain a proper tray design. Finally, the number of iterations for thedesign method is checked against a maximum (default 30) to prevent a continuousloop.

The adjustment factorsf1, f2, andf3 are percentile in/decrements, normally set at 5, 2,and 1 %. These factors – together with all the default, lower, and upper settings that areused in the design routine – are stored in a “design file” (TDESIGN.DEF, described inSection??) that can be tailored to handle specific kinds of designs and columns. Thisallows the selection of different methods for capacity and hydrodynamic calculationsas well. Also the fraction that the flows need to change before a re-design is issued canbe changed in this manner together with other design criteria. The design file must bein the current directory for the nonequilibrium program to use it, otherwise the normaldefaults will be used. To obtain the best results, it would be best to have differentTDESIGN.DEF files for distillation and absorption. However, a compromise betweenthese operations was struck andChemSepcurrently has one file to handle both.

18.5.2 Tray Column Design: Pressure drop

The same design routine for a tray design at a specific fraction of flood may also beused to design a tray with a certainmaximumpressure drop, using a default fraction offlood of 75%. Note that this method of designing trays does not fix the pressure drop:it only applies a maximumallowed pressure drop over the tray. If the tray designresults in a pressure drop larger than that specified the layout is adjusted accordingto the steps for excessive pressure drop per Table18.4. To obtain a layout which hasa lower pressure drop is to raise the bubbling area, in effect lowering the fraction offlood. However, the weir height is also lowered and the hole diameter is increased(albeit with a smaller factor).

18.5.3 Packed Column Design: Fraction of flooding

For packed columns only the column diameter is to be estimated. Default packingdata are used for all parameters that are not specified; values of 1” metal Pall rings

470

Table 18.4: Tray design checks and adjustments

Problem Test AdjustmentsBubble cap vapor distribution hlg/hd > 0.5 p + f1,

hskirt + f2,hslot + f3,dh − f3

Weeping Frh/(2/3) < 1− fa

free < 0.05Ab < Abf : Ab = Abf

Wf + f1

else: Ab − f1

dh − f3

hw − f3

tv + f2 (vt)Hydrodynamic (downcomer) flooding) Ts < hdb/FF Ts + f1

Ad + f1

hw + f2

hc + f3

Excessive liquid entrainment Ab + f1

Ts + f1

dh − f2

hw − f3

Froth height limit hf > 0.75Ts Ab + f1

Ts + f2

hw − f3

Excessive pressure drop gρhwt > ∆pmax Ab + f1

hw − f1

dh + f2

p + f1 (bc)hskirt + f2 (bc)hslot + f3 (bc)

Excessive vapor entrainment Ad + f1

471

for random packed sections and of Koch Flexipack 2 (316SS) for structured sections.To determine the packed column diameter, the diameter that gives rise to the floodingpressure drop (as specified) is computed using the selected pressure drop model. Theresulting diameter is corrected for the fraction of flooding and the system factor:

Dc =Dc,flood√FF SF

(18.137)

This makes the resulting column diameter depend on the selected pressure drop model.If no pressure drop model is selected the Leva (1992) model is selected (which is afunction only of the packing factor). If no pressure drop at flood is specified, it isestimated with Kister and Gill correlation (1992):

∆Pflood = 0.115F 0.7p (18.138)

(with pressure drop as liquid height and English units!). This correlation is a functiononly of the packing factor but has been tested on a wide range of packings and anaccuracy of 15 %. As long as the packing factor is known, this design method will notfail.

18.5.4 Packed Column Design: Pressure drop

Tray design based on a specified pressure drop is done as discussed above but with adefault fraction of flooding of 75 %. However, the specified pressure drop functionsas a maximum allowed pressure drop per tray. No adjustment is done if the pressuredrop is below this specified pressure drop.

Packed column design automatically finds the diameter leading to the specified pres-sure drop (with the selected pressure drop model). This is done by using a linear searchtechnique as the different packing pressure drop correlations can behave quite errati-cally. The maximum allowed pressure drop is the flooding pressure drop as specifiedor computed from Kister’s correlation and the packing factor. If the pressure drop isspecified to be very low the column diameter might converge to unrealistic diameters.A zero or larger than flooding pressure drop specification results in a 70 % fraction offlooding design.

18.6 Comparison with Experimental Distillation Data

Here, we illustrate the performance of the nonequilibrium model by simulating sev-eral systems for which experimental data is available in the literature. We focus our

472

attention on ternary systems; only in mixtures with more than two species can themolecular interaction between them influence the mass transfer resulting in differentindividual component Murphree efficiencies.

The complete process of comparing experimental data with the current version ofChemSephas been automated and provides a test for the correct behavior of the sim-ulator. We hope to build up an extensive database of distillation experiments andwelcome additional data. The experimental literature data is entered in a database filethat consists of keywords and the data. Then we carry out simulations and store eachsimulation in a sep-file. With the use of some utility programs we convert the simula-tion information and compare it to the experimental measured values. We can createparity plots and calculate average and maximum errors.

18.6.1 Ternary Distillation Experiments

The experiments discussed below were carried out at total reflux in columns withbubble-cap trays.

Vogelpohl (1979) has reported some results for the distillation of two non-ideal sys-tems: acetone, methanol, and water as well as methanol, isopropanol, and water. Theexperiments were done in a column with 38 bubble-cap trays of 0.3 m in diameter.Due to the ease of separation, only up to 13 trays were active for the experimentalruns. The experimental data clearly shows that the component Murphree efficien-cies are unequal; indeed, in the acetone-methanol-water system the composition ofmethanol passes through a maximum in the column and the efficiency for this compo-nent becomes unbounded. Vogelpohl shows that the assumption of equal componentefficiencies gives rise to large differences between the predicted and measured com-position profiles.

The simulations were done using the total reflux mode of the nonequilibrium model.For total reflux specifications one must use a column configuration with a condenserand reboiler plus one feed. Either the distillate flow is set to zero and a reboiled vaporflow is specified, or, the bottoms flow is set to zero and a reflux flowrate is specified.Only these specifications of the column operation will trigger the total reflux modeof the column simulator. In this mode the feed specifications are employed as thespecification of the vapor or liquid compositions on a specific stage. The compositions(and stage) that are to be fixed are set by the feed compositions and stage. Thus, ifwe know the compositions of the vapor leaving the reboiler we specify a feed to thereboiler and set the feed component flows equal to the known mole fractions. Toindicate that these are vapor mole fractions I set the vapor fraction of the feed as 1.On the other hand, if the liquid reboiler compositions are known we would specify the

473

feed vapor fraction as 0.

For Vogelpohl’s data the compositions of the vapor leaving the (total) reboiler werespecified to match the measured values. The reboiler vapor flowrate was specified at0.65kmol/h resulting in an effective F-factor around 0.1. The calculated fraction offlood was around 20 %. Table18.5shows the UNIQUAC interaction parameters usedfor the acetone, methanol, and water column. These interaction parameters were fittedto binary VLE data. The bubble-cap trays were specified with 0.3m tray diameter,tray spacing as 0.2m, bubbling area of 0.06008m2, a weir height of 0.03m, and aflow path width of 0.24m. The other layout parameters are assigned/computed by thesimulator. The AIChE MTC model was used together with the vapor plug flow andliquid mixed flow models.

Table 18.5: UNIQUAC interaction parameters (cal/mol) for the Acetone (1) -Methanol (2) - Water (3) system

Components i-j Aij Aji

acetone - methanol 403.8524 -84.2364acetone - water 698.7989 -110.382methanol - water -337.129 549.2958

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

Mol

e fr

actio

n

�

Stage Number

Rn run number n (1) acetone(2) methanol

R1(1)

R1(2)R2(1)

R2(2)

R3(1)

R3(2)

Figure 18.1: Experimental compositions (points) and the predicted composition pro-files (lines) for the acetone-methanol-water system.

474

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Sim

ulat

ed c

ompo

sitio

ns�

Experimental compositions

"Acetone""Methanol"

"Water"

Figure 18.2: Parity plot for the acetone-methanol-water system.

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12 14

Mol

e fr

actio

n

�

Stage Number

Rn run number n (1) methanol(2) isopropanol

R1(1)

R1(2)

R3(1)

R3(2)

Figure 18.3: Experimental compositions (points) and the predicted composition pro-files (lines) for the methanol-isopropanol-water system.

475

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Sim

ulat

ed c

ompo

sitio

ns�

Experimental compositions

"Methanol""Isoprop"

"Water"

Figure 18.4: Parity plot for the methanol-isopropanol-water system.

For the methanol, isopropanol, and water column UNIQUAC interaction parameterswere taken from DECHEMA (p. 575) that were fitted to ternary VLE data, see Ta-ble18.6. The same bubble-cap tray layout, column specifications, and model selec-tions were used as for the acetone-methanol-water column.

Figure18.1shows the measured compositions and the simulated mole fraction profilesfor the acetone-methanol-water system. Figure18.2 shows that the nonequilibriummodel does an excellant job in predicting the mole fractions for this very nonidealsystem. Figure18.3and Figure18.4show that the methanol-isopropanol-water sys-tem is predicted less well. We suspect this may be due to the interaction parametersof the activity coefficients. These simulations are extremely sensitive to these param-eters, especially as isopropanol is going through a maximum in concentration. Theaverage and maximum discrepancies in the predicted and experimentally measuredcompositions are shown in Table18.8.

Ternary distillation experiments using acetone, methanol, and ethanol were performedby Free and Hutchison (1960) in a column with 7 bubble-cap trays of 0.1016m in di-ameter. They also find that equal Murphree efficiencies cannot explain the bevaviorof this system. Twelve runs were conducted covering different regions of the ternarycomposition triangle. The column they used had a tray diameter of 0.1016m, bub-bling area of 0.00689m2, 0.015m weir height and a flow path length of 0.0813m.

476

Table 18.6: UNIQUAC interaction parameters (cal/mol) for the Methanol (1) - Iso-propanol (2) - Water (3) system

Components i-j Aij Aji

methanol - isopropanol 754.216 -457.107methanol - water 670.563 -442.713isopropanol - water 355.536 28.874

The F-factor was assumed to be around 0.9√

kg/m/s and a vapor boilup of 0.65kmol/h was specified, resulting in fraction of flood around 35 %. Table18.7showsthe UNIQUAC Q prime interaction parameters were used (Prausnitz et al., 1980). TheUNIQUAC Q prime activity coefficient model gives excellent results for these exper-iments. Figure18.5shows the data and the predicted column profiles for some of theexperimental runs. The agreement is excellent, as can also be seen from the parityplot, Figure18.6.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8

Mol

e fr

actio

n

�

Stage Number

Rn run number n (1) acetone(2) methanol

R4(1)

R4(2)R9(1)

R9(2)

R11(1)

R11(2)

Figure 18.5: Comparison of experimental compositions (points) and the predictedcomposition profiles (lines) for the acetone-methanol-ethanol system.

All these simulations were done by specifying the bottom compositions in the column,just as was done by Krishnamurthy and Taylor (1985). The errors in Table18.8wouldbe reduced if we would specify the compositions in the middle of the column, as theerrors in the predicted mole fractions often accumulate from stage to stage.

477

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Sim

ulat

ed c

ompo

sitio

ns�

Experimental compositions

"Acetone""Methanol"

"Ethanol"

Figure 18.6: Comparison of experimental and predicted mole fractions for theacetone-methanol-ethanol system.

Table 18.7: UNIQUAC interaction parameters (cal/mol) for the Acetone (1) -Methanol (2) - Ethanol (3) system

Components i-j Aij Aji

acetone - methanol 359.10 -96.90acetone - ethanol 404.49 -131.25methanol - ethanol 660.19 -292.39

Table 18.8: Summary of the average and maximum discrepancies between modelprediction and experimental measurement

System No. of No. of Average MaximumRuns Samples Error Error

acetone - methanol - water 3 22 0.015 0.070methanol - isopropanol - water 3 27 0.024 0.087acetone - methanol - ethanol 12 67 0.010 0.051

478

18.6.2 Significance of Multicomponent Interaction Effects

Figure18.7is a comparison for the acetone-methanol-water experiments of the nonequi-librium model with an ‘equal diffusivity’ model. This model uses a single averagevalue of the diffusion coefficients for each component. It yields equal component stageefficiencies and, therefore, corresponds to the conventional equilibrium stage modelwith efficiencies. The comparison clearly shows that the predicted top compositions ofthe ‘equal diffusivity’ model are qualitatively different from the experimental values.

This can be explained by inspecting the back-calculated Murphree component effi-ciencies of the nonequilibrium model, see Figure18.8. We see that the efficiencies ofwater and acetone differ by about 10%! This explains the observed 10% differencein top compositions. The methanol efficiencies show an even more weird behavior:they becomeunboundedbetween plate 6 and 7. When we look at the compositions,we see that the reason for this is that methanol goes through a maximum around stage6. Whenever a component goes through an extreme in composition (the driving forcebecomes zero) and there is still mass transfer occurring (however little) than the effi-ciencies are unbounded. If we had more stages in the column, we would observe thatthe methanol efficiency below this maximum stays at the higher value of the Murphreeefficiency of water. Apparently, thedirectionof the mass transfer is important!

18.6.3 Binary Distillation Experiments: Mass Transfer Coefficientsand Flow Models

To illustrate the behavior of the various tray MTC models as well as the differentflow models we include here some comparisons with experimental data of the FRI byYanagi and Sakata (1979, 1981). Two systems were used in these tests: the cyclo-hexane -n-heptane system at pressures of 28, 34, and 165kPa, and thei-butane -n-butane system at pressures of 1138, 2056, and 2756kPa. The experiments werecarried out in sieve tray columns operated at total reflux. Nonequilibrium simulationswere done for a column with the same tray design (the design parameters are sum-marized in Table18.9) at total reflux (Kooijman, 1995). The Murphree efficiencieswere calculated for each component on each tray from the results of a simulation andaveraged (over those trays not adjacent to condenser/reboiler). Simulations were doneusing different combinations of flow models:

• Mixed vapor - Mixed liquid

• Plug flow vapor - Mixed liquid

• Plug flow vapor - Plug flow liquid

479

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

Mol

e fr

actio

n�

Stage Number

Rn run number n (1) acetone(2) methanol

R1(1)

R1(2)

Figure 18.7: Experimental compositions (points) and the predicted composition pro-files for the acetone-methanol-water system using the nonequilibrium model (solidlines) and the ‘equal diffusivity’ model (broken lines).

Table 18.9: Sieve Plate Dimensions of FRI Column

Column diameter (m) 1.2Tray spacing (m) 0.61Sieve plate material 316SSPlate thickness (mm) 1.5Hole diameter (mm) 12.7Hole pitch (mm) 30.2Weir length (m) 0.94Weir height (mm) 25.4,50.8Downcomer clearance (mm) 22,38Effective bubbling area (m2) 0.859Hole area (m2) 0.118

Simulations were carried out with flows that go from 20% to 100% of flooding. Fig-ure 18.9 shows some of these results with the Chan and Fair (1984) mass transfercoefficients correlations. The experimental efficiencies show a decline at low andhigh fractions of flooding, probably due to weeping and liquid entrainment. The Chan

480

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8

Mur

phre

e E

ffic

ienc

y

Stage Number

acetone

methanol

water

Figure 18.8: Back-calculated Murphree component efficiencies for the acetone-methanol-water system from the nonequilibrium simulation.

and Fair model includes a quadratic dependence of NV on the fraction of floodingin order to account for the decrease in mass transfer at both low and high fractions offlooding. For this reason the Chan and Fair method usually describes the mass transfer(and hence, the efficiencies) better than the other mass transfer coefficient models.

Note that the Mixed-Mixed flow model underpredicts the efficiencies, as is true forthe Plug flow vapor - Mixed flow liquid model. The Plug-Plug flow model fits theexperimental efficiencies quite well. This should not be too surprising as this datawas actually used in the development of the Chan and Fair correlations. We are,however, using the correlations in a nonequilibrium model rather than in an efficiencycalculation.

Four different methods for estimating the binary mass transfer coefficients for sievetrays were tested: AIChE (1958), Chan and Fair (1984), Zuiderweg (1982), and Chenand Chuang (1994). Figure18.10shows the results for the i-butane/n-butane testsusing the plug-plug flow model. In general, the AIChE and the Chan-Fair correlationsbehave in similarly, except for the strong dependence on the fraction of flooding ofthe Chan-Fair model. This is not surprising since both use the same expression for theliquid mass transfer coefficients. The Zuiderweg and Chen-Chuang models predicthigher efficiencies as they have higher values for the liquid number of transfer units

481

0 20 40 60 80 100 Fraction of flooding (%)

�

100

80

60

40

20

0

Mur

phre

e E

ffic

ienc

y (%

)�

Figure 18.9: Murphree efficiencies for different flow models for a (8% hole area) sievetray column with the cyclohexane -n-heptane system operating at 165kPa. Mixed-Mixed flow (thick dotted line), Plug flow vapor - Mixed flow Liquid (thick dashedline), and Plug-Plug flow (solid line). Mass transfer coefficients from the Chan andFair correlation..

than the first two correlations. For this test they perform well; in many other teststhese two models tend to overpredict the Murphree efficiencies.

The Chan-Fair correlation tends to describes the overall behavior of the Murphree ef-ficiencies better than the other methods considered. However, it’s formulation causesit always to have a maximum efficiency at 60% fraction of flood. This limits themodel to sieve trays only and to the range of fractions of flooding where the quadraticterm is positive (0-1.2). Presumably, the fall-off in tray performance at low and highfractions of flooding is due to increases in weeping or entrainment at these extremeflows. It is not clear to us that mass transfer coefficient correlations should account forthese effects. Rather, we suggest that these effects should be separated. We have alsoencountered situations where the Chan and Fair correlations provide negative masstransfer coefficients because the flows are outside it’s range. Not only are negativemass transfer coefficients physically meaningless, they may prevent the program thatimplements our nonequilibrium model from converging to a solution! Despite these

482

0 20 40 60 80 100 Fraction of flooding (%)

�

120

100

80

60

40

20

0

Mur

phre

e E

ffic

ienc

y (%

)�

Figure 18.10: Murphree efficiencies for different Mass Transfer Coefficient modelsfor a (14% hole area) sieve tray column withi-butane -n-butane system operating at1138kPa. Chan and Fair (thick dotted line), AIChE (thick dashed line), Zuiderweg(dashed line), and Chen and Chuang (solid line)..

problems with the Chan and Fair method we think its limitations are less serious (fromour perspective) than are the limitations of other methods and, for now, it is our methodof choice.

Symbol List

Latin Symbols

ad interfacial area density (m2/m3)a area (m2)Ah hole area (m2)Ab, Abub bubbling area (m2)Ad downcomer area (m2)

483

B packing base (m)c number of components,

molar concentration (kmol/m3)Ca Capillary numberdh hole diameter (m)deq equivalent diameterD binary diffusivity coefficient (m2/s)Dc column diameter (m)De eddy dispersion coefficient (m2/s)f1, f2, f3 design adjustment factorsFp packing factor (1/m)Fs F factorFs = Uv

√ρV (kg0.5/m0.5/s)

FF fraction of floodingFP flow parameterFP = ML/MV

√ρV

t /ρLt

Fr Froude numberg gravitational constant, 9.81 (m/s2)hc clearance height under downcomer (m)hcl clear liquid height (m)hd dry tray pressure drop height (m)hdb downcomer backup liquid height (m)hf froth height (m)hi liquid height at tray inlet (m)hlg liquid gradient pressure drop height (m)hl, hL liquid pressure drop height (m)how height of liquid over weir (m)hr residual pressure drop liquid height (m)hwt wet tray pressure drop liquid height (m)hw weir height (m)hudc liquid height pressure loss under downcomer (m)k binary mass transfer coefficient (m/s)Le Lewis number (Le = Sc/Pr)Mw molecular weight (kg/kmol)N number of transfer units, NTUP perimeter (m)p hole pitch (m),

pressure (Pa)∆p pressure drop (Pa)∆Pmax maximum design pressure drop (Pa/tray or Pa/m)Pr Prandtl numberQ volumetric flow (m3/s)Re Reynolds number

484

S packing side (m)Sc Schmidt numberSF system derating factort residence time (s)tv valve thickness (m)T temperature (K)Ts tray spacing (m)u, U velocity (m/s)V vapor flow rate (kmol/s)We Weber numberWl weir length (m)x liquid mole fractiony vapor mole fractionz mole fractionZ tray flow path length (m)

Greek Symbols

α fraction liquid in frothβ fractional free areaβ = Ah/Ab,ε void fractionΓ liquid flow per perimeterφ fractional entrainmentρ density (kg/m3)σ surface tension (N/m)η viscosity (Pa s)λ thermal conductivity (W/m/K)

Superscripts

I interfaceL liquidP phasePV vapor

485

Subscripts

b, bub bubblingc critical, contacteff effectivefl, flood at flooding conditionsi componentij stagej,

componentjh holeMW minimum wettingp packingspec specifiedt total

Abbreviations

bc bubble-caps

References

Bubble Tray Design Manual: Prediction of Fractionation Efficiency, AIChE, NewYork (1958).

P.E. Barker, M.F. Self, “The evaluation of Liquid Mixing Effects on a Sieve Plate usingUnsteady and Steady-State Tracer Techniques”,Chem. Eng. Sci., Vol. 17, (1962) p.541.

S.D. Barnicki, J.F. Davis, “Designing Sieve-Tray Columns, Part 1: Tray Design”,Chem. Engng., Vol. 96, No. 10 (1989) pp. 140–146.

S.D. Barnicki, J.F. Davis, “Designing Sieve-Tray Columns, Part 2: Column Designand Verification”,Chem. Engng., November (1989) pp. 202–212.

D.L. Bennett, R. Agrawal, P.J. Cook, “New Pressure Drop Correlation fo Sieve TrayDistillation Columns”,AIChE J., Vol. 29 (1983) pp. 434–442.

486

R. Billet, M. Schultes, ”Advantage in correlating packed column perfomance”,IChemE.Symp. Ser.No. 128 (1992) p. B129.

J.L Bravo, J.R. Fair, ”Generalized Correlation for Mass Transfer in Packed DistillationColumns”,Ind. Eng. Chem. Process Des. Dev., Vol. 21 (1982) pp. 162–170.

J.L. Bravo, J.A. Rocha, J.R. Fair, ”Mass Transfer in Gauze Packings”,HydrocarbonProcessing, January (1985) pp. 91–95.

J.L. Bravo, J.A. Rocha, J.R. Fair, ”Pressure Drop in Structured Packings”,Hydrocar-bon Processing, March (1986) pp. 45–48.

J.L. Bravo, J.A. Rocha, J.R. Fair, ”A Comprehensive Model for the Performance ofColumns Containing Structured Packings”,I. ChemE. Symp. Ser., No. 128 (1992) pp.A439–A457.

H. Chan, J.R. Fair, “Prediction of Point Efficiencies on Sieve Trays. 1. Binary Sys-tems”,Ind. Eng. Chem. Process Des. Dev., Vol. bf 23 (1984) pp. 814–819.

G.X. Chen and K.T. Chuang, “Prediction of Efficiencies for Sieve Trays in Distilla-tion”, Ind. Eng. Chem. Res., Vol. 32 (1993) pp. 701–708.

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